I just don't feel like our relationship is even.

Okay, so my partner works like 3-4, days a weeks at the moment concreting. I'm home with our son all day everyday, cooking, cleaning and tending to mother duties... All day long. When I go out I HAVE to take my son with me every single time. So, I asked my partner if he could look after our son so I could go and do the washing (our washing machine broke so I have to take the washing to my mothers house and do it all there). This is the first time in months I've asked him, I asked him specifically today because there are horrible bush fires around our town and there is ash raining from the sky and smog everywhere, I didn't want to take my baby out in that. He got crabby because he said he "couldn't be bothered" and "he's tired". This is his 3rd day off of work. He hasn't done anything. He is always alloed to go to his mates house 'just because' to relax for 3-4 house, drink and smoke while I am home with the baby or out with the baby 24/7. I never ever pester him. I don't care of he is home or not to be honest. He can go out, but I'd just think that he'd WANT to help me out? Give ME a break once in a while instead of being so all about him all the time. He always tried to compete about who's more tired? Can't we just be a team? He knows how hard it is at home because he can't even be home with the baby by himself for 10 minutes and he complains as soon as I walk though the door, like I went to buy butter before I left to do the washing and he goes: "He was crying the whole time you left" literally as soon as I walk through the door, I was gone for 5-10 minutes Like, YEAH, I that's what I have to look after all day, but he still doesn't want to give me a break sometimes? The only break I get is and hour or two a day whole my son sleeps and even then, I'm cleaning or cooking. He gets to go out and swim in his mates pool and drink and relax all the time WITHOUT the baby. And when I want a break away from our son (which never happens) he gets shitty? I just don't get it. There's no fucking equality. Am I right or wrong?